How do you simplify √75⋅√60?

1 Answer
Johnson Z.
Feb 1, 2016

30√5

Explanation:

Recall that a perfect square is the product of squaring a whole number.

For example:

22=4

32=9

52=25

62=36

When you simplify a radical, you must first break it down using perfect square numbers. For example, in your case:

√75⋅√60

=√25⋅3⋅√4⋅15

The square root of 25 is 5, so you can bring the 25 out of the square root sign and write a 5 instead. Similarly, the square root of 4 is 2, so you can also bring the 4 out of the square root sign and write a 2 instead.

=5√3⋅2√15

Multiply.

=(5⋅2)(√3⋅√15)

=10√45

Since √45 can be simplified even further:

=10√9⋅5

Simplify.

=10⋅3√5

=30√5

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